Question

A 200 g bullet is shot with an initial velocity of 630 m/s from a gun with a barrel length of 80 cm.


How long does the bullet take to travel the length of the barrel?

Answer 1

I know to find time, we use t= d/v

How do you get the velocity, I know for sure it is NOT 630 m/s?

Answer 2

I think that the quoted velocity is the velocity of the bullet just as it leaves the barrel?
Assume the bullet starts from zero velocity and undergoes a constant acceleration and reaches a velocity of 630 m/s at the end.
So use the relationship that the distance travelled is equal to the average speed times the time taken?

Answer 3

yes, it is common to speak of "muzzle velocity" or the velocity at which the projectile leaves the barrel.

so we know that in 80 cm the bullet goes from rest to 630 m/s. we also know that for constant acceleration from rest, displacement at time \(t\) is \[x=\frac{1}{2}at^2\] and velocity is \[v=at\]
we know \(x=80\text{ cm}\) when the bullet leaves the barrel, and that \(v=630\text{ m/s}\)

I think the trick here is to realize that \[x=\frac{1}2at^2\ = \frac{1}2 (at) t\]and you know the value of \(at\) at the time the bullet leaves the barrel, and the value of \(x\), so you should be able to find the value of \(t\)...don't forget to do unit conversions as needed!

another way of looking at it is that the average speed with constant acceleration from rest will be 1/2 of the maximum velocity. You know the length of the barrel and the maximum velocity, so finding the time is easy. Work it both ways and see that you get the same answer.

Answer 4

Ok thank you for your explanation.